1. With a straightedge, draw a triangle on a thin piece of cardboard.Draw the three medians of the triangle so that they intersect at one point.This point is called thecentroid.Now cut out the triangle and try to balance it on the end of a pencil or pen.It should easily balance.Why do you think the triangle is easy to balance at this point? Will the special points made by the altitudes, perpendicular bisectors, and angle bisectors balance as well? Describe your findings and explain why you think they did or did not happen.
2. Draw a triangle with verticesA,B, andC.Now extend the sides of the triangle so that you create threeexterior angles.What is the sum of these three exterior angles?Why do you think these three exterior angles have this sum? Describe your findings and explain why you think this happens.
3. Draw a right triangle and label its verticesA,B, andC.Now draw the altitude from the right angle so that it intersects thehypotenuse, the longest side of the right triangle.Label the point of intersection between the altitude and the hypotenuse pointD.You should see three right triangles.Are the three right triangles similar? Why or why not?